Case-studies and workflows

Initial Setup

library(tidyverse)
library(parallel)
library(CoRC)

# helper to run tasks in parallel on all cores
mapInParallel <- function(data, fun, ..., .prep = {}) {
  cl <- makeCluster(detectCores())
  clusterCall(cl = cl, fun = eval, .prep, env = .GlobalEnv)
  ret <- clusterApplyLB(cl = cl, x = parallel:::splitList(data, length(data)), fun = lapply, as_mapper(fun), ...)
  stopCluster(cl)
  flatten(ret)
}

3D trajectory plot of calcium model

This example loads the (Kummer2000 - Oscillations in Calcium Signalling) model. The model has 3 species which oscillate. These oscialltions can be visualized as a trajectory through a 3D space. The example does this once in a deterministic and once in a stochatic fashion.

loadSBML("http://www.ebi.ac.uk/biomodels-main/download?mid=BIOMD0000000329")
# Run 24 sec (2 Periods)
setTimeCourseSettings(24, intervals = 10000)

timeseries <- list(
  deterministic = runTimeCourse(),
  stochastic = runTimeCourse(method = list(method = "directMethod", Use.Random.Seed = T, Random.Seed = 1))
)

# simplify species names so they are valid R syntax
timeseries <- map(timeseries, set_tidy_names, TRUE)

# Create the same plot for both timeseries
plots <- map(
  timeseries,
  plotly::plot_ly,
  type = "scatter3d",
  mode = "lines",
  x = ~ G.alpha,
  y = ~ activePLC,
  z = ~ Calcium,
  color = ~ Time
)

unloadModel()

plots$deterministic

plots$stochastic

Statistics of repeated stochastic simulations

This implements an example from the (Condor-COPASI paper). The example illustrates advantages of parallel processing.

# Run 1000 stochastic time series possibly in parallel
loadModel("https://raw.githubusercontent.com/copasi/condor-copasi/master/examples/stochastic_test.cps")
# timeseries <- 1:1000 %>% map(~ runTimeCourse())
timeseries <-
  # Defines parallel evaluation:
  mapInParallel(
    # perpare worker (.prep),
    .prep = quote({
      library(CoRC)
      loadModel("https://raw.githubusercontent.com/copasi/condor-copasi/master/examples/stochastic_test.cps")
      setTimeCourseSettings(method = list(method = "directMethod", Use.Random.Seed = T))
    }),
    # iteration data (1000 random seeds),
    1:1000,
    # iteration code (formula ~)
    ~ runTimeCourse(method = list(method = "directMethod", Random.Seed = .x))
  )

# Combine all results and reshape the data
plotdata <-
  timeseries %>%
  bind_rows() %>%
  group_by(Time) %>%
  # calculate mean and sd for all time points
  summarise_all(funs(mean, sd)) %>%
  # gather all values so the column "name" identifies "a_mean", "b_sd" etc.
  gather("name", "value", -Time) %>%
  # split up information on species (a,b,c) and type of value (mean, sd)
  separate(name, c("species", "type"), "_") %>%
  spread(type, value)

sample_n(plotdata, 5)
#> # A tibble: 5 x 4
#>    Time species     mean       sd
#>   <dbl>   <chr>    <dbl>    <dbl>
#> 1 10.60       c 1.325675 2.548818
#> 2 14.85       c 1.200354 1.889224
#> 3 22.90       b 7.652909 5.774307
#> 4 36.30       b 8.749512 5.842988
#> 5  8.05       a 2.482888 3.862359

plot <-
  ggplot(data = plotdata, aes(x = Time, y = mean, group = species, tt_sd = sd)) +
  geom_ribbon(aes(ymin = mean - sd, ymax = mean + sd, fill = species), alpha = 1 / 4) +
  geom_line(aes(color = species)) +
  guides(fill = "none") +
  labs(
    x = paste0("Time (", getTimeUnit(), ")"),
    y = paste0("Concentration (", getQuantityUnit(), ")"),
    color = "Species"
  )

unloadModel()

plotly::ggplotly(plot, tooltip = c("group", "x", "y", "tt_sd"))

Parameter scan

2D scan over the cartesian product of two species concentration vectors

This implements an example from the (Mendes2009 paper) on COPASI use cases.

loadSBML("https://www.ebi.ac.uk/biomodels-main/download?mid=BIOMD0000000068")
setSteadyStateSettings(calculateJacobian = FALSE, performStabilityAnalysis = FALSE)

# Cartesian product of the input values
scan <- cross_df(
  list(
    cysteine = 0.3 * 10 ^ seq(0, 3, length.out = 6),
    adomed = seq(0, 100, length.out = 51)
  )
)

scan <-
  scan %>%
  mutate(
    # Calculate steady state fluxes for every row
    ss_fluxes = pmap(., function(cysteine, adomed) {
      setSpecies("Cysteine", initial.concentration = cysteine)
      setSpecies("adenosyl", initial.concentration = adomed)
      ss <- runSteadyState()
      stopifnot(ss$result == "found")
      ss$reactions$concentration.flux
    }),
    # The second flux is CGS
    CGS = map_dbl(ss_fluxes, 2),
    # The third flux is TS
    TS = map_dbl(ss_fluxes, 3)
  )

plot <-
  ggplot(data = scan, aes(x = adomed, group = cysteine)) +
  geom_point(aes(y = CGS, color = "CGS")) +
  geom_point(aes(y = TS, color = "TS")) +
  geom_line(aes(y = CGS, color = "CGS")) +
  geom_line(aes(y = TS, color = "TS")) +
  labs(
    x = paste0("Adomed (", getQuantityUnit(), ")"),
    y = paste0("Flux (", getQuantityUnit(), " / ", getTimeUnit(), ")"),
    color = "Species"
  )

unloadModel()

plotly::ggplotly(plot)

2D scan over random concentrations of two species

This implements an example from the (Mendes2009 paper) on COPASI use cases. It is in many ways similar to the previous example but is written to run parallelized.

loadSBML("https://www.ebi.ac.uk/biomodels-main/download?mid=BIOMD0000000068")

# 10000 repeats of steady state task with random cysteine and adomed
scan <-
  # Defines parallel evaluation:
  mapInParallel(
    # perpare worker (.prep),
    .prep = quote({
      library(CoRC)
      loadSBML("https://www.ebi.ac.uk/biomodels-main/download?mid=BIOMD0000000068")
      setSteadyStateSettings(calculateJacobian = FALSE, performStabilityAnalysis = FALSE)
    }),
    # iteration data (10000 random seeds),
    1:10000,
    # iteration code (formula ~)
    ~ {
      set.seed(.x)
      cysteine <- 0.3 * 10 ^ runif(1L, min = 0, max = 3)
      adomed <- runif(1L, min = 0, max = 100)
      setSpecies(
        key = c("Cysteine", "adenosyl"),
        initial.concentration = c(cysteine, adomed)
      )
      ss <- runSteadyState()
      stopifnot(ss$result == "found")
      list(
        cysteine = cysteine,
        adomed = adomed,
        CGS = ss$reactions$concentration.flux[2],
        TS = ss$reactions$concentration.flux[3]
      )
    }
  )

# Combine all results and reshape the data
plotdata <-
  scan %>%
  bind_rows() %>%
  gather("reaction", "flux", CGS, TS)

plot <-
  ggplot(data = plotdata, aes(x = adomed, y = flux, group = reaction, tt_cys = cysteine)) +
  geom_point(aes(color = reaction), alpha = 1 / 10, size = 3 / 4) +
  labs(
    x = paste0("Adomed (", getQuantityUnit(), ")"),
    y = paste0("Flux (", getQuantityUnit(), " / ", getTimeUnit(), ")"),
    color = "Species"
  )

unloadModel()

plotly::ggplotly(plot, tooltip = c("tt_cys", "x", "y"))

Parameter Estimation

This implements an example from the (Mendes2009 paper) on COPASI use cases.

loadSBML("http://www.ebi.ac.uk/biomodels-main/download?mid=BIOMD0000000010")

# get timeseries for the record
data_before <-
  runTimeCourse(1000, 1) %>%
  set_tidy_names(TRUE)

# read experimental data
data_experimental <-
  read_tsv("data/MAPKdata.txt") %>%
  rename(Time = time, "Mos-P" = "MAPKKK-P", "Erk2-P" = "MAPK-P") %>%
  set_tidy_names(TRUE)

# define the experiments for copasi
fit_experiments <- defineExperiments(
  data = data_experimental,
  type = c("time", "dependent", "dependent"),
  mapping = c(NA, species(c("Mos-P", "Erk2-P"), "Concentration")),
  weight_method = "mean_square"
)

# define the parameters for copasi
fit_parameters <-
  map(
    parameter(c("n).V1", "V2", "V5", "V6", "V9", "V10")),
    ~ {
      val <- getParameters(.x)$value
      defineParameter(parameter(.x, "Value"), lower.bound = val * 0.1, upper.bound = val * 1.9, start.value = val)
    }
  )

result <-
  runParamEst(
    parameters = fit_parameters,
    experiments = fit_experiments,
    method = "LevenbergMarquardt",
    updateModel = TRUE
  )

# get timeseries for the record
data_after <-
  runTimeCourse(1000, 1) %>%
  set_tidy_names(TRUE)

plots <- list(
  Erk2.P =
    ggplot(mapping = aes(x = Time, y = Erk2.P)) +
    geom_point(data = data_experimental, aes(color = "experimental")) +
    geom_line(data = data_before, aes(color = "before")) +
    geom_line(data = data_after, aes(color = "after")) +
    scale_color_manual(values = c(before = "red", after = "green", experimental = "black")) +
    labs(
      x = paste0("Erk2-P (", getQuantityUnit(), ")"),
      y = paste0("Time (", getTimeUnit(), ")"),
      color = "Series"
    ),
  Mos.P =
    ggplot(mapping = aes(x = Time, y = Mos.P)) +
    geom_point(data = data_experimental, aes(color = "experimental")) +
    geom_line(data = data_before, aes(color = "before")) +
    geom_line(data = data_after, aes(color = "after")) +
    scale_color_manual(values = c(before = "red", after = "green", experimental = "black")) +
    labs(
      x = paste0("Mos-P (", getQuantityUnit(), ")"),
      y = paste0("Time (", getTimeUnit(), ")"),
      color = "Series"
    )
)

# unloadModel()

result$fitted.values
#> # A tibble: 2 x 5
#>   fitted.value objective.value root.mean.square error.mean
#>          <chr>           <dbl>            <dbl>      <dbl>
#> 1      [Mos-P]        25.45444         1.681747 -0.2829374
#> 2     [Erk2-P]        10.08304         1.058460  0.3290446
#> # ... with 1 more variables: error.mean.std..deviation <dbl>
result$parameters
#> # A tibble: 6 x 8
#>                            parameter lower.bound start.value     value
#>                                <chr>       <dbl>       <dbl>     <dbl>
#> 1             (MAPKKK activation).V1       0.250   2.4643673 2.4643673
#> 2           (MAPKKK inactivation).V2       0.025   0.2465618 0.2465618
#> 3 (dephosphorylation of MAPKK-PP).V5       0.075   0.8817485 0.8817485
#> 4  (dephosphorylation of MAPKK-P).V6       0.075   1.4250000 1.4250000
#> 5  (dephosphorylation of MAPK-PP).V9       0.050   0.7280555 0.7280555
#> 6  (dephosphorylation of MAPK-P).V10       0.050   0.7070213 0.7070213
#> # ... with 4 more variables: upper.bound <dbl>, std..deviation <dbl>,
#> #   coeff..of.variation.... <dbl>, gradient <dbl>

plotly::ggplotly(plots$Erk2.P)

plotly::ggplotly(plots$Mos.P)